Subgroups — #15675679

Order 2944.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092822	C₂	1	2	yes	maximal
2	#13092245	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
4	#10625040	—	2	2	no	—
5	C₂×C₁₆×C₂₃	C₂²	1	2	yes	—
6	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	#10625000	—	2	2	no	—
8	#10625000	C₂²	1	4	yes	—
9	C₂×Dic₄₆	—	4	2	no	—
10	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
12	C₄²×C₂₃	D₄	1	1	yes	characteristic
13	C₄⋊Dic₂₃	—	2	4	no	—
14	C₄⋊Dic₂₃	—	4	2	no	—
15	C₁₆×C₂₃	Q₈	1	4	yes	complemented
16	C₂×C₄×C₂₃	D₈	1	2	yes	—
17	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
18	C₂×Dic₂₃	—	4	4	no	—
19	Dic₄₆	—	8	4	no	—
20	C₈×C₂₃	Q₁₆	1	2	yes	—
21	C₈×C₂₃	C₂×Q₈	1	2	yes	—
22	#2254	—	23	1	no	maximal, Sylow
23	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
24	C₄×C₂₃	SD₃₂	1	4	yes	—
25	C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
26	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
27	Dic₂₃	—	8	4	no	—
28	#500	—	23	2	no	—
29	#367	—	23	4	no	—
30	C₄×C₁₆	D₂₃	1	1	yes	characteristic
31	C₂×C₂₃	#500	1	1	yes	characteristic
32	C₂×C₂₃	C₂×SD₃₂	1	2	yes	—
33	C₄⋊Q₈	—	46	2	no	—
34	C₂×C₁₆	C₂×D₂₃	1	2	yes	—
35	#107	—	23	4	no	—
36	#107	—	46	2	no	—
37	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
38	C₂₃	#2254	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	92	2	no	—
40	C₂×C₈	D₉₂	1	1	yes	characteristic
41	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
42	C₄⋊C₄	—	46	4	no	—
43	C₄⋊C₄	—	92	2	no	—
44	C₄²	D₉₂	1	1	yes	characteristic
45	C₁₆	Dic₄₆	1	4	yes	complemented
46	Q₈	—	184	4	no	—
47	C₂×C₄	—	92	4	no	—
48	C₂×C₄	D₁₈₄	1	2	yes	—
49	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
50	C₈	Dic₉₂	1	2	yes	—
51	C₈	C₂×Dic₄₆	1	2	yes	—
52	C₂²	C₂×D₁₈₄	1	1	yes	characteristic
53	C₄	—	184	4	no	—
54	C₄	#10624982	1	4	yes	—
55	C₄	#10625040	1	1	yes	characteristic
56	C₄	C₂×Dic₉₂	1	1	yes	characteristic
57	C₂	#13092822	1	1	yes	characteristic
58	C₂	C₂×#10624982	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₈₄
commutator, cosocle	C₂×C₈×C₂₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₄×C₁₆×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₈
hypercenter	C₄×C₁₆	D₂₃
hypocenter	C₂₃	#2254
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
15. C₁₆×C₂₃	Q₈	semidirect
38. C₂₃	#2254	semidirect
45. C₁₆	Dic₄₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13092822	2
#13092245	2
C₄×C₁₆×C₂₃	2
#2254	23